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# Mensuration: Formulas & Solved Examples Notes | Study Quantitative Aptitude (Quant) - CAT

## Document Description: Mensuration: Formulas & Solved Examples for CAT 2022 is part of Quantitative Aptitude (Quant) preparation. The notes and questions for Mensuration: Formulas & Solved Examples have been prepared according to the CAT exam syllabus. Information about Mensuration: Formulas & Solved Examples covers topics like Areas, Volume and Mensuration: Formulas & Solved Examples Example, for CAT 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Mensuration: Formulas & Solved Examples.

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Areas

Areas of some well-known figures are given below:

Example.1 A horizontal pipe for carrying floodwater has a diameter of 1 m. When water in it is 10 cm deep then the width of water surface AB is equal to ________ cm.

(1) 10 cm
(2) 25 cm
(3) 60 cm
(4) 70 cm
(5) None

Correct Answer is Option (3).

• Let O be the centre of circle.
⇒ 502 = 402 + x2
⇒ 2500 – 1600 = x2
⇒ x2 = 900
⇒ x = 30
• ∴ AB = 2x = 60 cm.

Question for Mensuration: Formulas & Solved Examples
Try yourself:The area of quadrilateral PQRS is 228cm2. Find the length of QA.

Example.2 Area of the shaded region is:

Correct Answer is Option (1).

Volume

Length of a Diagonal

• The length of diagonal of a cuboid =
• The length of a diagonal of a cube =

Example.3 An insect is crawling to climb a 20 metre long pipe of diameter 3.5 metres. If the insect take 4 circular rounds to reach the top of the building, then what will be total distance (in nearer metres) traveled by insect to reach the top?
(1) 47 m
(2) 48 m
(3) 49 m
(4) 50 m

• Since the insect is moving in circular way, so it will cover the distance which will be 4 times the distance of the longest side AB of a right angled triangle. In the figure AO is equal to the circumference of the pipe.
AO = πd =   = 11m
BO = 5 m
AB =  =  = 12.08 m
• Total distance traveled = 12.08 × 4 = 48.32 m
• Hence distance in nearer meters = 48 m

Question for Mensuration: Formulas & Solved Examples
Try yourself:What is the volume of a cone having radius of 21cm and height of 5cm?

Example.4 The surface area of a cube is 726 sq metres. Find the volume of the cube
(1) 1234 m2
(2) 1431 m2
(3) 1341 m3
(4) 1331 m3
(5) None of these

Correct Answer is Option(4).

• Surface area S = 726 m2 Volume V = ?
• In a cube,
• S = 6a2 = 726 ⇒ a2 = 121 ⇒ a = 11 m
• So, V = a3 = 113 = 1331 m3.
The document Mensuration: Formulas & Solved Examples Notes | Study Quantitative Aptitude (Quant) - CAT is a part of the CAT Course Quantitative Aptitude (Quant).
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